Charmonium in the vector channel at finite temperature from QCD sum rules

Abstract

Thermal Hilbert moment QCD sum rules are used to obtain the temperature dependence of the hadronic parameters of charmonium in the vector channel, i.e. the $J/\ensuremath{\psi}$ resonance mass, coupling (leptonic decay constant), total width, and continuum threshold. The continuum threshold ${s}_{0}$, which signals the end of the resonance region and the onset of perturbative QCD, behaves as in all other hadronic channels, i.e. it decreases with increasing temperature until it reaches the perturbative QCD threshold ${s}_{0}=4{m}_{Q}^{2}$, with ${m}_{Q}$ the charm quark mass, at $T\ensuremath{\simeq}1.22{T}_{c}$. The rest of the hadronic parameters behave very differently from those of light-light and heavy-light quark systems. The $J/\ensuremath{\psi}$ mass is essentially constant in a wide range of temperatures, while the total width grows with temperature up to $T\ensuremath{\simeq}1.04{T}_{c}$ beyond which it decreases sharply with increasing $T$. The resonance coupling is also initially constant and then begins to increase monotonically around $T\ensuremath{\simeq}{T}_{c}$. This behavior of the total width and of the leptonic decay constant provides a strong indication that the $J/\ensuremath{\psi}$ resonance might survive beyond the critical temperature for deconfinement.